International
Tables for Crystallography Volume H Powder diffraction Edited by C. J. Gilmore, J. A. Kaduk and H. Schenk © International Union of Crystallography 2018 |
International Tables for Crystallography (2018). Vol. H, ch. 3.6, pp. 291-292
Section 3.6.2.6.3. Optical elements^{a}Department of Civil, Environmental and Mechanical Engineering, University of Trento, via Mesiano 77, 38123 Trento, Italy |
The equation of Caglioti et al. (1958), modified by Rietveld (1969) and originally developed for constant-wavelength neutron diffraction, is frequently employed for parameterization of the instrumental profile. The FWHM and the pV mixing parameter η (replacing the Lorentzian and Gaussian widths of the Voigt) are then parameterized according to functions in tan(θ) and θ, respectively (Caglioti et al., 1958; Leoni et al., 1998; Scardi & Leoni, 1999), The parameters of the Fourier transform of a Voigt or pseudo-Voigt are then constrained to those of equations (3.6.18) and (3.6.19). This is particularly convenient, as the Fourier transform of a Voigtian is analytical. In fact, for the pV case we havewhere σ = FWHM/2 and where (Langford & Louër, 1982; Scardi & Leoni, 1999)Equation (3.6.18) can be found in the literature in a different form and with additional terms accounting, for example, for size effects: besides forcing a symmetry of the profile in 2θ space, these extra terms are a contradiction as they have nothing to do with the instrument itself.
References
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